Given the data: Use Excel and MATLAB to: (a) Calculate f(3.4) using Newton\'s in

Question

Given the data: Use Excel and MATLAB to: (a) Calculate f(3.4) using Newton's interpolating polynomials of order 1 through 3. Choose the sequence of the points for your estimates to attain the best possible accuracy. That is, the points should be centered around and as close as possible to the unknown. (b) Repeat (a) but use the Lagrange polynomial. The following data define the sea-level concentration (o) of dissolved oxygen for fresh water as a function of temperature (T): Use MATLAB to fit the data with a fifth-order polynomial Display the results graphically. Use the fifth-order polynomial to estimate o(27) and comment and compare the interpolated value from the exact value. Note that the exact result is 7.986 mg/L.

Explanation / Answer

Exersice 1:

Newton interpolation algorithm

Exersice 2:

we can use any of the above graphs for solutions and then plot the graph.

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